Modric has hardly set La Liga alight since his £33million move from Tottenham last summer and media speculation has linked him with a move back to England with Manchester United, Manchester City or Chelsea.
However, Alonso, who joined Madrid in 2009 after five years in the Barclays Premier League with Liverpool, believes Modric needs to be given time to settle in and is convinced the Croatia international will be a success at the nine-time European champions.
"I don't think it's pressure. He plays in a position where we have several players and he's adapting to a new club and a new league. It took me a while to adapt on my return to La Liga," Alonso told reporters on Tuesday.
"But he's integrated very well, he's a fantastic guy and a great player. I've no doubt that he's going to be an important player."
Alonso was also asked his thoughts on the relationship between Madrid coach Jose Mourinho and goalkeeper Iker Casillas.
Mourinho has caused a huge stir in Spain after omitting long-serving number one and club captain Casillas from his starting line-up for the last two matches, selecting Antonio Adan in his place.
Madrid fans jeered Mourinho prior to Sunday's home league match with Real Sociedad, which the reigning champions won 4-3 despite Adan being sent off after only six minutes, with Casillas taking his place.
"He (Casillas) seems fine to me. He's not used to being a substitute but he's working hard to be ready when he's needed to play. And with the coach he was a respectful, cordial relationship," Alonso said.
"The team trust in both Iker and Adan. The other day Adan was unlucky to be sent off in the sixth minute and Iker could do little about the goals he conceded. All other things else are technical decisions that we completely respect."